# Thread: AS Level mechanics - 2 Particles moving together

1. ## AS Level mechanics - 2 Particles moving together

A motorcyclist M leaves a road junction at time t=0s. She accelerates at a rate of 3ms-2 for 8s and then maintains the speed she has reached. A car C leaves the same road junction as M at time t=os. The car accelerates from rest to 30ms-1 in 20s and then maintains the speed of 30ms-1. C passes M as they both pass a pedestrian.

Find the distance of the pedestrian from the road junction

2. ## Re: AS Level mechanics - 2 Particles moving together

Firstly, lay out UVAST for the acceleration parts of the motorcyclist and car and fill in any gaps using the UVAST equations. So you need to work out the final velocity and distance for the motorcyclist and the acceleration and distance for the car.
As we have different times for both the car and motorcyclist, I would suggest working out how far the motorcyclist has travelled after 20 seconds so both are at the same time - makes working out much easier. Don't forget that for the remaining 12 seconds of the motorcyclist it is no longer accelerating but moving at a constant speed.
Now you know how far they have both travelled after 20 seconds you can set up an equation like this:

Total distance travelled by motorcyclist in 20 seconds + (Velocity x t) = Total distance travelled by car in 20 seconds + (Velocity x t)

Don't forget that the velocity is now constant. T represents the number of seconds after 20 seconds that the car and motorcyclist meet. Solve the equation and find t. Add it to 20 seconds and that is the time where they pass the pedestrian.

You need the distance, however, so you can form another UVAST list for either the motorcyclist or car to work this out (car should be easier!) for just the constant speed part. Use this to work out the distance but don't forget to add it to the distance for the accelerating part!

I hope that that makes sense and that it doesn't sound like a load of waffle! Let me know if you need clarification on any of the points. Good luck!

3. ## Re: AS Level mechanics - 2 Particles moving together

Is that the whole question? It's just that (having recently studied this sort of thing) it seems to me to be directing you towards a speed-time graph. I think you could draw an s-t graph and then work out the area underneath either of the lines, which would tell you the total distance travelled by the car/motorcycle.